Preheat grill or grill pan on stovetop to medium-high heat.
Brush onion slices with oil and place on pan. Cook the slices, turning once, until well browned and softened. Remove from heat and let cool for 3 to 5 minutes. Chop finely and set aside.
In small bowl, add 2 ounces smoked blue cheese, mayonnaise, paprika and cayenne. Stir to thoroughly combine and set aside.
In large bowl, add 2 ounces smoked blue cheese, ground beef, ground pork and black pepper. Mix with hands to thoroughly combine. Separate into 12 portions and form into burger patties. Salt the outside of each patty lightly. Grill until done; internal temperature should reach 160° F.
While the burgers are cooking, place slider buns on the upper warming rack of grill or into the oven to warm.
To serve, place each slider on a pre-warmed bun and top with grill sauce. Sprinkle with additional blue cheese, to taste.